Sharp transitions in the image cannot be well represented by time domain data which is sampled for a finite amount of time. Since real data must be truncated at some point in time, any discontinuity in the image will include an overshoot which is 9% of the magnitude of the discontinuity. This overshoot appears as "ringing" in the image. This ringing near sharp transitions is often referred to as the "Gibbs artifact" after Josiah W. Gibbs. Gibbs noted that with more coefficients the value of the overshoot in using the Fourier series does not diminish. However, the error (i.e., the overshoot) becomes confined to a region that shrinks around the discontinuity as the sampling time is increased. This causes the artifact to become less prominent.
Accordingly, the size of the sampling window used in obtaining the imaged data is increased, the amplitude of the overshoot remains the same, but the overshoot is compressed towards the edge of the discontinuity. However, taking more sampling points requires more time which reduces throughput. Also, as is well known, the signal-to-noise ratio (SNR) is proportional to the inverse of the square root of N where N is the number of sampling points used. Thus, taking more sampling points reduces the SNR while improving the spatial resolution.
In magnetic resonance image contrast resolution is often preferred over spatial resolution. Thus, reduced sampling in the phase encoding direction which reduces acquisition time should be preferred; especially since in the time saved the SNR could be improved by averaging several measurements. However, in the past the reduced sampling increased the ringing artifact cancelling any benefits of the improved SNR. Thus, until the invention U.S. Pat. No. 4,950,991, imaging experts have been reluctant to use low resolution images because of the increased Gibbs artifact.
The U.S. Pat. No. 4,950,991 uses a multiplicative filter in the time domain to reduce the amplitude of the overshoot and increase the SNR. The filter is used in conjunction with asymmetrical sampling and complex conjugation. The asymmetrical sampling and complex conjugation increases the spatial resolution based on a given number of actual sampling points. The filter reduces the spatial resolution of the image. However, the reduction in the spatial resolution of the filter is offset in the patent by the increase in spatial resolution afforded by the use of asymmetrical sampling and complex conjugation. Thus, the previously mentioned patent obtained a reduction in Gibbs artifact without adversely affecting the spatial resolution, the SNR or the scan time. It has now been found that the suppression of the ringing or truncation artifacts can be further improved and with no adverse effect on the resolution, the SNR or the scan time.
The improvement herein comprises the means and methods for optimizing the selection of system controllable parameters, i.e., the filter characteristics and the asymmetry of the sampling.